STAT 400
Spring 2012
Homework #4
(10 points)
(due Friday, Feb 17, by 3:00 p.m.)
No credit will be given without supporting work.
1.
Suppose a discrete random variable
X
has the following probability distribution:
P(
X =
k
) =
!
2
ln
k
k
,
k
= 1, 2, 3, … .
Recall
( Homework #1 Problem 6 ):
This is a valid probability distribution.
a)
Find
X
=
E
(
X
)
by finding the sum of the infinite series.
b)
Find the momentgenerating function of
X,
M
X
(
t
).
c)
Use
M
X
(
t
)
to find
X
=
E
(
X
).
d)
Find
X
2
=
Var
(
X
).
2.
The number of typos made by a student follows Poisson distribution with the rate
of 1.5 typos per page.
Assume that the numbers of typos on different pages are
independent.
a)
Find the probability that there are at most 2 typos on a page.
b)
Find the probability that there are exactly 10 typos in a 5page paper.
c)
Find the probability that there are exactly 2 typos on each page in a 5page paper.
d)
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 Spring '08
 Kim
 Statistics, Probability, Tom, Discrete probability distribution

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